Olympic Data
1 Import the data
NOC Year Decade ID First.Name Name Last.Name Sex Age
1 AFG 1960 1960s 59346 Mohammad Mohammad Asif Khokan Khokan M 24
2 AFG 1960 1960s 59043 Faiz Faiz Mohammad Khakshar Khakshar M 18
3 AFG 1960 1960s 109486 Abdul Abdul Hadi Shekaib Shekaib M 20
Height Weight BMI BMI.Category Team Population GDP GDPpC
1 171 78 26.67487 3 Afghanistan 8996973 537777800 59.77319
2 162 52 19.81405 0 Afghanistan 8996973 537777800 59.77319
3 178 68 21.46194 2 Afghanistan 8996973 537777800 59.77319
Games Season City Sport Event
1 1960 Summer Summer Roma Wrestling Wrestling Men's Middleweight, Freestyle
2 1960 Summer Summer Roma Wrestling Wrestling Men's Flyweight, Freestyle
3 1960 Summer Summer Roma Athletics Athletics Men's 100 metres
Medal Medal.No.Yes
1 No Medal 0
2 No Medal 0
3 No Medal 0
[ reached 'max' / getOption("max.print") -- omitted 3 rows ]'data.frame': 151977 obs. of 24 variables:
$ NOC : Factor w/ 122 levels "AFG","ALB","AND",..: 1 1 1 1 1 1 1 1 1 1 ...
$ Year : int 1960 1960 1960 1960 1960 1960 1960 1960 1960 1960 ...
$ Decade : Factor w/ 6 levels "1960s","1970s",..: 1 1 1 1 1 1 1 1 1 1 ...
$ ID : int 59346 59043 109486 59102 128736 29626 39922 106372 128736 58364 ...
$ First.Name : Factor w/ 14118 levels "","A","A.","Aadam",..: 8716 3731 64 599 64 11978 64 4634 64 8716 ...
$ Name : Factor w/ 74268 levels " Gabrielle Marie \"Gabby\" Adcock (White-)",..: 48941 19066 218 3341 220 64832 215 23793 220 48946 ...
$ Last.Name : Factor w/ 47370 levels "","-)","-Alard)",..: 23228 23112 38893 23137 44908 13260 16633 37860 44908 22890 ...
$ Sex : Factor w/ 2 levels "F","M": 2 2 2 2 2 2 2 2 2 2 ...
$ Age : int 24 18 20 35 20 28 22 23 20 20 ...
$ Height : int 171 162 178 166 179 168 172 170 179 166 ...
$ Weight : num 78 52 68 66 75 73 70 58 75 62 ...
$ BMI : num 26.7 19.8 21.5 24 23.4 ...
$ BMI.Category: Factor w/ 5 levels "0","1","2","3",..: 4 1 3 3 3 4 3 3 3 3 ...
$ Team : Factor w/ 332 levels "Acipactli","Afghanistan",..: 2 2 2 2 2 2 2 2 2 2 ...
$ Population : int 8996973 8996973 8996973 8996973 8996973 8996973 8996973 8996973 8996973 8996973 ...
$ GDP : num 5.38e+08 5.38e+08 5.38e+08 5.38e+08 5.38e+08 ...
$ GDPpC : num 59.8 59.8 59.8 59.8 59.8 ...
$ Games : Factor w/ 30 levels "1960 Summer",..: 1 1 1 1 1 1 1 1 1 1 ...
$ Season : Factor w/ 2 levels "Summer","Winter": 1 1 1 1 1 1 1 1 1 1 ...
$ City : Factor w/ 29 levels "Albertville",..: 19 19 19 19 19 19 19 19 19 19 ...
$ Sport : Factor w/ 51 levels "Alpine Skiing",..: 51 51 3 51 3 51 3 3 3 51 ...
$ Event : Factor w/ 489 levels "Alpine Skiing Men's Combined",..: 478 468 17 476 33 482 22 24 18 466 ...
$ Medal : Factor w/ 4 levels "Bronze","Gold",..: 3 3 3 3 3 3 3 3 3 3 ...
$ Medal.No.Yes: Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...Number of sports per year at the https://www.topendsports.com/events/summer/sports/number.htm1
There is clearly an upward trend, but no seasonal pattern. The data is also a little choppy at the beginning. Part of the explanation is that the data points are not evenly spaced. Most Olympic games are 4 years apart, but a few of them are just 2 years apart, and during World War I and World War II there were 8-year and 12-year gaps, respectively. Since time series data should be evenly spaced over time, we’ll only look at data from 1948 on, when the Olympics started being held every 4 years without any interruptions.
2 Creating models
I’m going to try 4 different models.
\[ y_{\text{linear}}(x) = ax+b \\ y_{\text{quadratic}}(x) = ax^2 + bx + c \\ y_{\text{exponential}}(x) = a\exp(bx) + c \\ y_{\text{cubic}}(x) = ax^3 + bx^2 + cx + d \]
And I’ll be able to use ANOVA to test the nested models: linear vs quadratic, and exponential growth vs s-curve (sigmoid).
Now I will try the model fits on the number of events per Olympic Games data.
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 17 | 33.33158 | NA | NA | NA | NA |
| Exponential | 16 | 32.28073 | 1 | 1.050847 | 0.5208539 | 0.4808924 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 17 | 33.33158 | NA | NA | NA | NA |
| Quadratic | 16 | 30.41244 | 1 | 2.919136 | 1.5357588 | 0.2331213 |
| Cubic | 15 | 29.04971 | 1 | 1.362737 | 0.7036577 | 0.4147260 |
3 Sports
3.1 Top 10 Sports
Year Mean_Weight StdDev_Weight Mean_Height StdDev_Height Sport Sex
1 1924 64.00000 0.000000 167.0000 0.000000 Swimming F
2 1956 61.00000 4.780914 169.7333 3.634491 Swimming F
3 1960 62.73469 5.619073 169.3469 6.839076 Swimming F
4 1964 63.06000 6.466270 171.3600 4.378799 Swimming F
5 1968 62.45455 5.361348 170.3636 4.583033 Swimming F
6 1972 60.23611 5.491333 170.3889 4.949194 Swimming F'data.frame': 339 obs. of 7 variables:
$ Year : int 1924 1956 1960 1964 1968 1972 1976 1980 1984 1988 ...
$ Mean_Weight : num 64 61 62.7 63.1 62.5 ...
$ StdDev_Weight: num 0 4.78 5.62 6.47 5.36 ...
$ Mean_Height : num 167 170 169 171 170 ...
$ StdDev_Height: num 0 3.63 6.84 4.38 4.58 ...
$ Sport : Factor w/ 10 levels "Basketball","Canoeing",..: 9 9 9 9 9 9 9 9 9 9 ...
$ Sex : Factor w/ 2 levels "F","M": 1 1 1 1 1 1 1 1 1 1 ...
3.2 Medalists
| Medal | mean |
|---|---|
| Bronze | 25.55859 |
| Gold | 25.28269 |
| No Medal | 24.93049 |
| Silver | 25.48383 |
# A tibble: 6 x 3
# Groups: Year [3]
Year Sex mean.Age
<int> <fct> <dbl>
1 1960 F 21.6
2 1960 M 26.0
3 1964 F 21.5
4 1964 M 25.7
5 1968 F 20.5
6 1968 M 25.1
3.3 Swimming
3.3.1 Female Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 8.508555 | NA | NA | NA | NA |
| Exponential | 12 | 8.161454 | 1 | 0.3471001 | 0.5103504 | 0.4886515 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 8.5085546 | NA | NA | NA | NA |
| Quadratic | 12 | 3.3398817 | 1 | 5.168673 | 18.57074 | 0.0010150 |
| Cubic | 11 | 0.6470143 | 1 | 2.692867 | 45.78190 | 0.0000309 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 11.69717 | NA | NA | NA | NA |
| Exponential | 12 | 11.34729 | 1 | 0.3498782 | 0.3700035 | 0.5543414 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 11.697173 | NA | NA | NA | NA |
| Quadratic | 12 | 5.842805 | 1 | 5.854368 | 12.02375 | 0.0046521 |
| Cubic | 11 | 2.432617 | 1 | 3.410188 | 15.42046 | 0.0023647 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 4.326164 | NA | NA | NA | NA |
| Exponential | 12 | 4.408289 | 1 | -0.0821246 | -0.223555 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 4.326164 | NA | NA | NA | NA |
| Quadratic | 12 | 4.163567 | 1 | 0.162597 | 0.4686279 | 0.5066258 |
| Cubic | 11 | 2.732882 | 1 | 1.430686 | 5.7585885 | 0.0352509 |
3.3.2 Male Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 3.720714 | NA | NA | NA | NA |
| Exponential | 12 | 3.559721 | 1 | 0.1609931 | 0.5427161 | 0.475466 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 3.7207136 | NA | NA | NA | NA |
| Quadratic | 12 | 1.8313700 | 1 | 1.889344 | 12.37987 | 0.0042351 |
| Cubic | 11 | 0.4074947 | 1 | 1.423875 | 38.43639 | 0.0000672 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 13.00892 | NA | NA | NA | NA |
| Exponential | 12 | 12.95885 | 1 | 0.0500719 | 0.046367 | 0.8331264 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 13.008921 | NA | NA | NA | NA |
| Quadratic | 12 | 12.927824 | 1 | 0.0810975 | 0.0752771 | 0.7884689 |
| Cubic | 11 | 2.535541 | 1 | 10.3922832 | 45.0851030 | 0.0000331 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 10.26588 | NA | NA | NA | NA |
| Exponential | 12 | 10.76283 | 1 | -0.4969448 | -0.5540679 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 10.265883 | NA | NA | NA | NA |
| Quadratic | 12 | 4.739344 | 1 | 5.526539 | 13.993175 | 0.0028181 |
| Cubic | 11 | 3.544380 | 1 | 1.194964 | 3.708575 | 0.0803623 |
3.4 Athletics
3.4.1 Female Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 4.210569 | NA | NA | NA | NA |
| Exponential | 12 | 4.285409 | 1 | -0.0748399 | -0.2095666 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 4.210569 | NA | NA | NA | NA |
| Quadratic | 12 | 3.883503 | 1 | 0.3270661 | 1.010632 | 0.3345930 |
| Cubic | 11 | 1.057545 | 1 | 2.8259583 | 29.394066 | 0.0002097 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 24.06089 | NA | NA | NA | NA |
| Exponential | 12 | 24.02365 | 1 | 0.0372406 | 0.018602 | 0.8937751 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 24.06089 | NA | NA | NA | NA |
| Quadratic | 12 | 17.52401 | 1 | 6.536879 | 4.476290 | 0.0559590 |
| Cubic | 11 | 13.83787 | 1 | 3.686136 | 2.930182 | 0.1149498 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 8.095579 | NA | NA | NA | NA |
| Exponential | 12 | 8.097702 | 1 | -0.0021235 | -0.0031468 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 8.095579 | NA | NA | NA | NA |
| Quadratic | 12 | 8.085980 | 1 | 0.0095987 | 0.0142450 | 0.9069711 |
| Cubic | 11 | 7.974949 | 1 | 0.1110312 | 0.1531475 | 0.7030196 |
3.4.2 Male Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 0.9457009 | NA | NA | NA | NA |
| Exponential | 12 | 0.9332067 | 1 | 0.0124942 | 0.1606617 | 0.695593 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 0.9457009 | NA | NA | NA | NA |
| Quadratic | 12 | 0.7883551 | 1 | 0.1573458 | 2.395050 | 0.1476766 |
| Cubic | 11 | 0.6019224 | 1 | 0.1864327 | 3.407016 | 0.0919830 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 20.30145 | NA | NA | NA | NA |
| Exponential | 12 | 20.31487 | 1 | -0.0134131 | -0.0079231 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 20.30145 | NA | NA | NA | NA |
| Quadratic | 12 | 20.29326 | 1 | 0.0081908 | 0.0048435 | 0.9456622 |
| Cubic | 11 | 13.12999 | 1 | 7.1632736 | 6.0012249 | 0.0322607 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 3.276112 | NA | NA | NA | NA |
| Exponential | 12 | 3.329318 | 1 | -0.0532056 | -0.191771 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 3.276112 | NA | NA | NA | NA |
| Quadratic | 12 | 2.659483 | 1 | 0.6166295 | 2.782328 | 0.1211719 |
| Cubic | 11 | 2.106053 | 1 | 0.5534296 | 2.890585 | 0.1171633 |
3.5 Gymnastics
3.5.1 Female Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 35.59138 | NA | NA | NA | NA |
| Exponential | 12 | 35.36262 | 1 | 0.2287617 | 0.0776283 | 0.7852807 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 35.591383 | NA | NA | NA | NA |
| Quadratic | 12 | 4.159030 | 1 | 31.4323530 | 90.691399 | 0.0000006 |
| Cubic | 11 | 3.733688 | 1 | 0.4253421 | 1.253121 | 0.2868053 |
3.5.2 Male Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 14.16465 | NA | NA | NA | NA |
| Exponential | 12 | 14.07826 | 1 | 0.0863857 | 0.0736333 | 0.79073 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 14.164646 | NA | NA | NA | NA |
| Quadratic | 12 | 2.872336 | 1 | 11.292310 | 47.176841 | 0.0000173 |
| Cubic | 11 | 1.627689 | 1 | 1.244646 | 8.411377 | 0.0144390 |
3.6 Rowing
3.6.1 Female Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 4.149078 | NA | NA | NA | NA |
| Exponential | 8 | 4.234549 | 1 | -0.0854708 | -0.1614733 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 4.149078 | NA | NA | NA | NA |
| Quadratic | 8 | 2.336048 | 1 | 1.8130300 | 6.208878 | 0.0374193 |
| Cubic | 7 | 1.559452 | 1 | 0.7765967 | 3.485954 | 0.1041248 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 15.83480 | NA | NA | NA | NA |
| Exponential | 8 | 16.00342 | 1 | -0.1686178 | -0.0842909 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 15.834804 | NA | NA | NA | NA |
| Quadratic | 8 | 2.320446 | 1 | 13.5143582 | 46.592285 | 0.0001342 |
| Cubic | 7 | 1.926398 | 1 | 0.3940476 | 1.431861 | 0.2704117 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 9.424177 | NA | NA | NA | NA |
| Exponential | 8 | 9.656112 | 1 | -0.2319344 | -0.1921556 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 9.424177 | NA | NA | NA | NA |
| Quadratic | 8 | 1.104136 | 1 | 8.3200410 | 60.2827063 | 0.0000541 |
| Cubic | 7 | 1.008614 | 1 | 0.0955226 | 0.6629479 | 0.4423346 |
3.6.2 Male Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 1.923962 | NA | NA | NA | NA |
| Exponential | 12 | 1.872159 | 1 | 0.0518021 | 0.3320367 | 0.5751109 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 1.923962 | NA | NA | NA | NA |
| Quadratic | 12 | 1.510689 | 1 | 0.4132727 | 3.2827891 | 0.0950925 |
| Cubic | 11 | 1.462089 | 1 | 0.0485994 | 0.3656368 | 0.5576592 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 19.88407 | NA | NA | NA | NA |
| Exponential | 12 | 20.63138 | 1 | -0.7473091 | -0.4346635 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 19.884073 | NA | NA | NA | NA |
| Quadratic | 12 | 5.894874 | 1 | 13.9891993 | 28.477351 | 0.0001775 |
| Cubic | 11 | 5.256667 | 1 | 0.6382065 | 1.335498 | 0.2723140 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 7.273221 | NA | NA | NA | NA |
| Exponential | 12 | 7.634802 | 1 | -0.3615807 | -0.5683144 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 7.273221 | NA | NA | NA | NA |
| Quadratic | 12 | 2.012381 | 1 | 5.260840 | 31.3708479 | 0.0001160 |
| Cubic | 11 | 1.845598 | 1 | 0.166783 | 0.9940485 | 0.3401819 |
3.7 Basketball
3.7.1 Female Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 4.141973 | NA | NA | NA | NA |
| Exponential | 8 | 4.189668 | 1 | -0.0476956 | -0.0910728 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 4.141973 | NA | NA | NA | NA |
| Quadratic | 8 | 3.810224 | 1 | 0.3317491 | 0.6965451 | 0.4281641 |
| Cubic | 7 | 3.797734 | 1 | 0.0124897 | 0.0230211 | 0.8836825 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 17.87967 | NA | NA | NA | NA |
| Exponential | 8 | 18.09276 | 1 | -0.213091 | -0.0942215 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 17.87967 | NA | NA | NA | NA |
| Quadratic | 8 | 14.74145 | 1 | 3.138222 | 1.703074 | 0.2281701 |
| Cubic | 7 | 12.24426 | 1 | 2.497190 | 1.427635 | 0.2710586 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 18.31425 | NA | NA | NA | NA |
| Exponential | 8 | 18.54528 | 1 | -0.2310301 | -0.099661 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 9 | 18.314246 | NA | NA | NA | NA |
| Quadratic | 8 | 10.723460 | 1 | 7.590785 | 5.662937 | 0.0445670 |
| Cubic | 7 | 8.311638 | 1 | 2.411823 | 2.031219 | 0.1971233 |
3.7.2 Male Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 4.943144 | NA | NA | NA | NA |
| Exponential | 12 | 4.922646 | 1 | 0.0204985 | 0.0499694 | 0.8268768 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 4.943144 | NA | NA | NA | NA |
| Quadratic | 12 | 4.892514 | 1 | 0.0506298 | 0.1241811 | 0.7306549 |
| Cubic | 11 | 4.335635 | 1 | 0.5568795 | 1.4128668 | 0.2596093 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 78.62687 | NA | NA | NA | NA |
| Exponential | 12 | 80.66841 | 1 | -2.041543 | -0.3036941 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 78.62687 | NA | NA | NA | NA |
| Quadratic | 12 | 66.59475 | 1 | 12.03212 | 2.16812 | 0.1666358 |
| Cubic | 11 | 30.06034 | 1 | 36.53441 | 13.36906 | 0.0037784 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 25.76692 | NA | NA | NA | NA |
| Exponential | 12 | 26.84673 | 1 | -1.079811 | -0.482656 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 25.766919 | NA | NA | NA | NA |
| Quadratic | 12 | 8.389214 | 1 | 17.3777050 | 24.8572104 | 0.0003168 |
| Cubic | 11 | 7.934290 | 1 | 0.4549246 | 0.6307017 | 0.4438938 |
3.8 Fencing
3.8.1 Female Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 12.21269 | NA | NA | NA | NA |
| Exponential | 12 | 12.21715 | 1 | -0.0044544 | -0.0043752 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 12.212691 | NA | NA | NA | NA |
| Quadratic | 12 | 5.825501 | 1 | 6.3871898 | 13.1570266 | 0.0034681 |
| Cubic | 11 | 5.491448 | 1 | 0.3340534 | 0.6691473 | 0.4307124 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 17.00640 | NA | NA | NA | NA |
| Exponential | 12 | 16.74273 | 1 | 0.2636671 | 0.1889778 | 0.6714834 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 17.00640 | NA | NA | NA | NA |
| Quadratic | 12 | 12.67503 | 1 | 4.331365 | 4.100690 | 0.0657024 |
| Cubic | 11 | 11.45006 | 1 | 1.224974 | 1.176824 | 0.3012066 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 16.51064 | NA | NA | NA | NA |
| Exponential | 12 | 16.66480 | 1 | -0.1541545 | -0.1110037 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 16.51064 | NA | NA | NA | NA |
| Quadratic | 12 | 15.77139 | 1 | 0.7392517 | 0.5624755 | 0.4677146 |
| Cubic | 11 | 10.19087 | 1 | 5.5805213 | 6.0236018 | 0.0320006 |
3.8.2 Male Athletes
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 15.32277 | NA | NA | NA | NA |
| Exponential | 12 | 15.33475 | 1 | -0.011983 | -0.0093771 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 15.322770 | NA | NA | NA | NA |
| Quadratic | 12 | 8.207974 | 1 | 7.114796 | 10.401781 | 0.0072842 |
| Cubic | 11 | 7.147501 | 1 | 1.060473 | 1.632067 | 0.2277214 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 14.71278 | NA | NA | NA | NA |
| Exponential | 12 | 14.86734 | 1 | -0.1545598 | -0.1247511 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 14.71278 | NA | NA | NA | NA |
| Quadratic | 12 | 14.08288 | 1 | 0.6299021 | 0.5367385 | 0.4778544 |
| Cubic | 11 | 11.92883 | 1 | 2.1540485 | 1.9863245 | 0.1863646 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 5.329521 | NA | NA | NA | NA |
| Exponential | 12 | 5.537634 | 1 | -0.2081129 | -0.4509788 | 1 |
| Models | Res.Df | Res.Sum Sq | Df | Sum Sq | F value | Pr(>F) |
|---|---|---|---|---|---|---|
| Linear | 13 | 5.329521 | NA | NA | NA | NA |
| Quadratic | 12 | 3.072275 | 1 | 2.2572456 | 8.8165764 | 0.0117170 |
| Cubic | 11 | 2.869575 | 1 | 0.2027005 | 0.7770159 | 0.3969078 |
References
1 R. Wood, (2010).